Free Energy and Diffusivity in the Fokker-Planck Theory of Polymer Translocation

TL;DR

This study combines simulations and theoretical analysis to understand free energy, diffusivity, and translocation times of charged polymers passing through nanopores, revealing deviations from classical polymer dynamics theories.

Contribution

It introduces a modified free energy formulation accounting for entropic effects and characterizes the scaling of diffusivity with polymer length, contrasting with Rouse theory predictions.

Findings

Scaling of mean translocation time with polymer length and voltage.

Modified free energy landscape incorporating entropic contributions.

Diffusivity scaling deviates from Rouse theory predictions.

Abstract

We revisit the Fokker-Planck based theory of driven polymer translocation through a narrow nanopore. A bead-spring model of a uniformly charged polyelectrolyte chain translocating through a semi-implicit model of a nanopore embedded in a membrane are used to gain insights into the underlying free energy landscape and kinetics of translocation. The free energy landscape is predicted using metadynamics simulation, an enhanced sampling method. A direct comparison with the theoretical free energy formulation proposed in the literature allows us to introduce a modification related to the entropic contribution in the theory. Additional classical Langevin dynamics simulation runs are performed to obtain the translocation time distribution for polymers of lengths $N$ driven by voltages $V$ through nanopores of radii $r_p$. In agreement with earlier reports, a scaling of the mean translocation time $\langle \tau_\text{LD} \rangle \sim N^\alpha/V$ is observed, with $\alpha \sim 1.40 - 1.48$ depending on the nanopore size. Fitting the mean first passage time given by the Fokker-Planck theory, $\langle \tau_\text{FP}\rangle$,to simulation results helps gain insights into the diffusivity $k_\text{FP}$ used in the theory. We report a scaling of $k_\text{FP}\sim N^\beta$. The $r_p-$dependent values of the exponent $\beta$ significantly deviate from the Rouse theory prediction of $\beta = -1$ for center-of-mass diffusivity of a polymer chain.